Plane and Solid Geometry |
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Page xi
... . 217 225 SOLID GEOMETRY Book VI . Lines and Planes in Space . Polyedral Angles 234 BOOK VII . Polyedrons , Cylinders , and Cones 270 BOOK VIII . The Sphere . 327 + 1 | V SYMBOLS AND ABBREVIATIONS is equivalent to xi.
... . 217 225 SOLID GEOMETRY Book VI . Lines and Planes in Space . Polyedral Angles 234 BOOK VII . Polyedrons , Cylinders , and Cones 270 BOOK VIII . The Sphere . 327 + 1 | V SYMBOLS AND ABBREVIATIONS is equivalent to xi.
Page 269
... its vertices lie in a plane . Ex . 1080. The common perpendicular is the shortest distance that can be drawn between two straight lines not in the same plane . BOOK VII POLYEDRONS , CYLINDERS , AND CONES POLYEDRONS 530. POLYEDRAL ANGLES ...
... its vertices lie in a plane . Ex . 1080. The common perpendicular is the shortest distance that can be drawn between two straight lines not in the same plane . BOOK VII POLYEDRONS , CYLINDERS , AND CONES POLYEDRONS 530. POLYEDRAL ANGLES ...
Page 270
... . DEF . A convex polyedron is one , every section of which is a convex polygon . NOTE . All the polyedrons treated of in this book are convex . PRISMS AND PARALLELOPIPEDS 534. DEF . A prism is a. 270 Polyedrons, Cylinders, and Cones.
... . DEF . A convex polyedron is one , every section of which is a convex polygon . NOTE . All the polyedrons treated of in this book are convex . PRISMS AND PARALLELOPIPEDS 534. DEF . A prism is a. 270 Polyedrons, Cylinders, and Cones.
Page 312
... = S T T " = 2 TRH 2 πR'H ' 2 TR ' ( H ' + R ' ) V πR2H R2 H R3 H3 X TR2H ' R12 H ' ( Why ? ) R H + R R2 H2 = X = - R H ' + R ' R12 H129 ( Why ? ) = R'3 H13 ( Why ? ) Q.E D. CONES 641. DEF . A conical surface is a surface 312 SOLID GEOMETRY.
... = S T T " = 2 TRH 2 πR'H ' 2 TR ' ( H ' + R ' ) V πR2H R2 H R3 H3 X TR2H ' R12 H ' ( Why ? ) R H + R R2 H2 = X = - R H ' + R ' R12 H129 ( Why ? ) = R'3 H13 ( Why ? ) Q.E D. CONES 641. DEF . A conical surface is a surface 312 SOLID GEOMETRY.
Page 313
... cone is a solid bounded by a conical surface and a plane cutting all its elements . 646. DEF . The lateral area of the cone is the conical sur- face ; the base of the cone is the plane surface ; the vertex ... cone is a cone whose. CONES 313.
... cone is a solid bounded by a conical surface and a plane cutting all its elements . 646. DEF . The lateral area of the cone is the conical sur- face ; the base of the cone is the plane surface ; the vertex ... cone is a cone whose. CONES 313.
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Common terms and phrases
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Popular passages
Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 180 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 328 - Every section of a sphere made by a plane is a circle.
Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.